This note removes technical assumptions and characterizes relatively dominated representations.
problem Geometrically finiteness and Anosov conditions in higher-rank settings.
method Characterization using eigenvalue gaps and limit maps.
result Relatively dominated representations are characterized using eigenvalue gaps and limit maps.
Characterizes Anosov representations and strongly convex cocompact groups with eigenvalue gaps.
problem Understanding Anosov representations and their properties.
method Characterizations via equivariant limit maps, Cartan property, and uniform gap summation.
result Characterizations of Anosov representations and strongly convex cocompact subgroups.
Study shows how to count and equidistribute cusped Hitchin representations with entropy gaps.
problem Counting and equidistribution of cusped Hitchin representations.
method Renewal theorem of Kesseböhmer and Kombrink applied to count and equidistribute.
result Entropy gaps at infinity allow for counting and equidistribution results.
Develops correlation number for specific potentials and Hitchin representations.
problem Analyzing correlation numbers for potentials with entropy gaps and Hitchin representations.
method Defines a correlation number for pairs of cusped Hitchin representations and explores its connection to the Manhattan curve.
result Establishes a connection between the correlation number and the Manhattan curve, revealing rigidity properties.
The paper explains what affects the generalization gap in visual RL with and without distractors.
problem Understanding what affects the generalization gap in visual reinforcement learning.
method Theoretical analysis and empirical evidence.
result Minimizing representation distance between training and testing environments reduces the generalization gap.
New metric explains neural network performance, simplifying generalization error calculation.
problem Precise characterization of neural network generalization error.
method Introducing Representation Gap, linking to intrinsic dimension and equivariant diffusion models.
result Asymptotic equivalent of Representation Gap is governed by intrinsic dimension, easy to estimate.
WR-CP reduces prediction set size and coverage gap under distribution shift.
problem Guaranteed coverage under distribution shift not achievable with i.i.d. assumption.
method Wasserstein distance, probability measure pushforwards, importance weighting, regularized representation learning.
result Reduces coverage gap to 3.2% across different confidence levels.
This paper evaluates fairness in deep metric learning and proposes a method to reduce subgroup performance gaps.
problem The negative impact of deep metric learning representations on minority subgroup performance in downstream tasks.
method Definition of fairness in DML through inter-class, intra-class, and uniformity properties; finDML benchmark; Partial Attribute De-correlation (PARADE) method.
result Bias in DML representations propagates to downstream tasks, even with balanced training data.
Chaos in cerebellar cells enhances complexity of neural patterns.
problem Understanding how cerebellar granular layer represents complex information.
method Constructed a model of cerebellar granular layer with gap junctions, evaluated using reservoir computing.
result Chaotic dynamics in the cerebellar granular layer produce complex and diverse output patterns.
New method learns disentangled representations using Gromov-Monge maps.
problem Learning disentangled representations from unlabelled data.
method Introduces a novel approach based on Gromov-Monge maps to preserve geometric features while aligning data distributions.
result Demonstrates effectiveness on four benchmarks, outperforming other methods.
The paper describes correlations of spectra for higher rank Anosov representations.
problem Understanding correlations of spectra for Anosov representations of higher rank groups.
method Relates correlation problem to counting projections in truncated hypertubes.
result Extends previous work on rank one representations to higher rank.
A new screening test for Lasso improves solution speed.
problem Improving the efficiency of Lasso solution methods.
method Safe region with dome geometry based on dual cutting half-spaces.
result The new screening test leads to significant acceleration.
Network representation learning (NRL) is a powerful technique for learning low-dimensional vector representation of high-dimensional and sparse graphs. Most studies explore the structure and metadata associated with the graph using random walks and employ an unsupervised or semi-supervised learning schemes. Learning in…
VAEs improve representation learning by inverting the data-generating process through self-consistency.
problem VAEs struggle to invert the data-generating process, yet often succeed in representation learning.
method Studied VAEs in the limit of near-deterministic decoders, proving self-consistency and showing ELBO convergence to a regularized log-likelihood.
result VAEs can perform independent mechanism analysis (IMA), recovering true latent factors under specific conditions.
Self-supervised learning performs better than supervised learning on imbalanced datasets.
problem The performance gap between balanced and imbalanced pre-training with self-supervised learning is smaller than with supervised learning.
method Systematic investigation of self-supervised learning under dataset imbalance, including experiments and theoretical analyses.
result Self-supervised representations are more robust to class imbalance than supervised representations.
This article presents the use of Answer Set Programming (ASP) to mine sequential patterns. ASP is a high-level declarative logic programming paradigm for high level encoding combinatorial and optimization problem solving as well as knowledge representation and reasoning. Thus, ASP is a good candidate for implementing p…
COBRA reduces modality gap in cross-modal tasks.
problem Joint embedding spaces fail to sufficiently reduce modality gap in multi-modal tasks.
method COBRA trains image and text modalities in a joint fashion using Contrastive Predictive Coding and Noise Contrastive Estimation.
result COBRA significantly reduces the modality gap and generates robust joint-embedding space.
Study estimates gaps in semigroup products, proving embedding properties.
problem Estimating singular value gaps in semigroup products.
method Lower estimates for singular value gaps of free products of semigroups in ping-pong position.
result Groups generated by semigroups in ping-pong position are quasi-isometrically embedded.
Data visualization and interaction with large data sets is known to be essential and critical in many businesses today, and the same applies to research and teaching, in this case, when exploring large and complex mathematical objects. GAP is a computer algebra system for computational discrete algebra with an emphasis…
A grand challenge in representation learning is to learn the different explanatory factors of variation behind the high dimen- sional data. Encoder models are often determined to optimize performance on training data when the real objective is to generalize well to unseen data. Although there is enough numerical eviden…
This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness -- in a sense specified in the paper -- of the risk measure's Kusuoka r…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including variants of multi-level methods and spectral clustering. We propose GAP, a Generaliz…
Geospatial analysis lacks methods like the word vector representations and pre-trained networks that significantly boost performance across a wide range of natural language and computer vision tasks. To fill this gap, we introduce Tile2Vec, an unsupervised representation learning algorithm that extends the distribution…
Estimates intrinsic dimension of data sets robustly to noise.
problem Estimating intrinsic dimension of noisy data sets.
method Quantum Cognition Machine Learning for data representation and spectral gap detection.
result Robust estimation of intrinsic dimension in the presence of Gaussian noise.
Uniformly random permutations converge to regular representation on surface groups.
problem Understanding the behavior of random homomorphisms to symmetric groups.
method Polynomial approximation and random walk analysis.
result Strong convergence of random representations to regular representation.
Unified framework for causal inference under sample selection.
problem Causal inference under sample selection with treatment and outcome non-randomness.
method ForestRiesz estimator, Riesz representation framework.
result ForestRiesz estimator yields more stable treatment effect estimates than conventional double machine learning approaches.
Paper aims to bridge semantic gap between ML and InfoSec by labeling malware datasets with behavioral features.
problem Semantic gap between ML and InfoSec communities hinders ML's impact in InfoSec.
method Surveyed existing malware datasets and features, labeled with behavioral features using threat reports.
result Behavioral labeling alters analysis from intent to executable behavior, bridging semantic gap.
We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system for generating atomic potentials through machine learning (ML). Tests on the QM7, QM7b and GDB9 biom…
Classifies prime algebraic tangles up to 14 crossings.
problem Classifying prime algebraic tangles systematically.
method Developed a novel canonical representation to distinguish mutant tangles.
result Increased classification of prime tangles up to 14 crossings.
New method improves image compression using bits-back coding.
problem Lossy image compression with deep latent variable models.
method Iterative inference, stochastic annealing, bits-back coding.
result New state-of-the-art performance on lossy image compression.
New bound proves rationality helps generalization in self-supervised learning.
problem Proving generalization gap in self-supervised learning.
method Proving upper bound on generalization gap for classifiers using rationality and self-supervised representations.
result Generalization gap tends to zero if classifier complexity is low relative to number of samples.
We define a class of representations of the fundamental group of a closed surface of genus 2 to PSL2(C): the pentagon representations. We show that they are exactly the non-elementary PSL2(C)-representations of surface groups that do not admit a Schottky decomposition, i.e. a…
GROOVE learns representations for weakly paired multimodal data.
problem Learning representations for high-content perturbation data with weakly paired samples.
method GroupCLIP contrastive loss integrated with an autoencoder framework.
result GROOVE performs on par with or outperforms existing approaches for cross-modal tasks.
RNNs struggle with in-context retrieval, while Transformers excel.
problem In-context retrieval capability of RNNs.
method Theoretical analysis and experimental techniques (CoT, RAG, Transformer layer).
result Enhancing RNNs with techniques improves their in-context retrieval capability, closing the representation gap with Transformers.
Gated attention improves model curvature, enhancing performance on nonlinear tasks.
problem Understanding the geometric implications of gating in attention mechanisms.
method Modeling attention outputs as Gaussian distributions and analyzing Fisher--Rao geometry.
result Gated attention enables non-flat geometries, including positively curved manifolds.
Paper tackles sample-efficient RL for linearly realizable MDPs with limited revisiting.
problem Sample-efficient reinforcement learning for linearly realizable MDPs with limited revisiting.
method Develops a new sampling protocol that allows for backtracking and revisiting states in a controlled manner.
result Achieves polynomial sample complexity scaling with feature dimension, horizon, and inverse sub-optimality gap.
Method constrains spectral gaps of hyperbolic spin surfaces using identities and semidefinite programming.
problem Bounding Laplacian and Dirac spectra of hyperbolic spin manifolds and orbifolds.
method Infinite family of spectral identities, semidefinite programming, and Selberg trace formula.
result Upper bounds on spectral gaps nearly saturated by specific orbifolds.
RedEx improves neural network optimization with convex optimization guarantees.
problem Difficult optimization of neural networks.
method RedEx architecture using convex optimization with semi-definite constraints.
result RedEx can efficiently learn functions fixed methods cannot.
New framework for RL with linear-convex models reduces performance gap.
problem Continuous-time episodic reinforcement learning with unknown coefficients and convex objectives.
method Probabilistic framework and phase-based learning algorithm for optimal exploration-exploitation trade-off.
result Sublinear regrets achieved, matching best possible results in literature.
We construct the spectral curve and the Baker--Akhiezer function for the Dirac operator which corresponds to the Clifford torus via the Weierstrass representation. By constructing this Baker--Akhiezer function we demonstrate a general procedure for constructing Dirac operators and their Baker--Akhiezer functions corres…
SupSiam and SupBYOL improve supervised representation learning with ANCL.
problem Improving supervised representation learning with ANCL.
method Proposed supervised ANCL framework leveraging labels to avoid collapse.
result Supervised ANCL improves representation learning across various datasets and tasks.
ProGraML uses graph-based machine learning to improve program optimization and analysis.
problem Improving program optimization and analysis with machine learning.
method Low-level, language agnostic graph representation and message passing neural networks.
result ProGraML achieves an average 94.0 F1 score on a benchmark dataset, significantly outperforming state-of-the-art approaches.
Electronic medical record (EMR) data contains historical sequences of visits of patients, and each visit contains rich information, such as patient demographics, hospital utilisation and medical codes, including diagnosis, procedure and medication codes. Most existing EMR embedding methods capture visit-code associatio…
Paper shows regularization improves robustness in domain generalization.
problem Improving robustness in domain generalization.
method Derives novel theoretical analysis to control representation smoothness and proposes a regularization method.
result Regularization improves robustness in domain generalization.
Foundation models improve wage gap decomposition by capturing omitted career history factors.
problem Estimating wage disparities using incomplete career history data.
method Fine-tuning foundation models to mitigate omitted variable bias and estimate wage gaps.
result Foundation models can decompose gender wage gaps more accurately than traditional econometric methods.
Trains word embeddings from music and text data to link music contexts.
problem Varying vocabulary size and musical relevance in word embeddings.
method Combines general text and music-specific data to train word embeddings.
result Trained embeddings better associate music contexts with compositions.
Adversarial training leads to clean data generalization with significant robust overfitting gap.
problem Significant robust generalization gap in adversarial training.
method Two theoretical views: representation complexity and training dynamics.
result ReLU nets with O(ND) extra parameters can achieve CGRO. Large mobility datasets collected from various sources have allowed us to observe, analyze, predict and solve a wide range of important urban challenges. In particular, studies have generated place representations (or embeddings) from mobility patterns in a similar manner to word embeddings to better understand the fun…